83.41.27 problem 9

Internal problem ID [19436]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise at end of chapter VIII. Page 141
Problem number : 9
Date solved : Monday, March 31, 2025 at 07:13:44 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+\left (x +2\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 12

ode:=x^2*diff(diff(y(x),x),x)-(x^2+2*x)*diff(y(x),x)+(x+2)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x \left ({\mathrm e}^{x} c_2 +c_1 \right ) \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 16

ode=x^2*D[y[x],{x,2}]-(x^2+2*x)*D[y[x],x]+(x+2)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x \left (c_2 e^x+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + (x + 2)*y(x) - (x**2 + 2*x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False